The invention is based on an injection onset adjusting apparatus in a fuel injection pump. The objective of an adjusting apparatus of this kind is to shift the injection onset to earlier at low engine rpm in order to improve starting, but at idling rpm to set a later injection onset and with increasing engine speed again to set an early injection onset. To this end, an adjusting apparatus of this generic type known for example from German Auslegeschrift No. 10 94 527 has in addition to the adjusting piston a coaxial supporting piston having a larger diameter than the adjusting piston, and a compression spring disposed between these pistons. The two ends of the adjusting piston and supporting piston remote from one another can be acted upon by the supply pressure of the fuel feed pump, in the case of the adusting piston via a check valve, and in the case of the support piston via an overpressure valve, so that only beyond a predetermined supply pressure is the support piston acted upon and displaced in the direction of a "late" injection onset, until it comes to a stop on a "late" injection onset, and until it comes to a standstill on a stop attached to the housing. As a result, with increasing rpm and correspondingly increasing supply pressure, the adjusting piston is displaced back toward an "early" injection onset, counter to the action of the compression spring.